Question

The domain of the function
$f\left(x\right)lo{g}_2\left(-lo{g}_{1/2}\left(1+\frac{1}{x^{1/4}}\right)-1\right)$ is

• A. $(0,1)$
• B. $(0,1]$
• C. $[1,\infty )$
• D. $(1,\infty )$

Answer 1

Answer: (A)

$f\left(x\right)$ is defined if - $lo{g}_{1/2}\left(1+\frac{1}{x^{1/4}}\right)-1>0$
$\Rightarrow lo{g}_{1/2}\left(1+\frac{1}{x^{1/4}}\right)<-1$
$\Rightarrow 1+\frac{1}{x^{1/4}}>{\left(\frac{1}{2}\right)}^{-1}$
$\Rightarrow \frac{1}{x^{1/4}}>1$
$\Rightarrow 0<x<1$